Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ι be given.
Assume H0: ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x1 x3 x4 = x2 x3 x4.
Apply encode_u_ext with
x0,
λ x3 . lam x0 (λ x4 . x1 x3 x4),
λ x3 . lam x0 (λ x4 . x2 x3 x4).
Let x3 of type ι be given.
Assume H1: x3 ∈ x0.
Apply encode_u_ext with
x0,
λ x4 . x1 x3 x4,
λ x4 . x2 x3 x4.
Let x4 of type ι be given.
Assume H2: x4 ∈ x0.
Apply H0 with
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.